Non homogeneous boundary value problems for linear dispersive equations

While the non-homogeneous boundary value problem for elliptic, hyperbolic and parabolic equations is relatively well understood, there are still few results for general dispersive equations. We define here a convenient class of equations comprising the Schrödinger equation, the Airy equation and linear ‘Boussinesq type’ systems, which is in some sense a generalization of strictly hyperbolic equations, and for which we define a generalized Kreiss-Lopatinskĭı condition. From the construction of generalized Kreiss symmetrizers (adapted from hyperbolic theory) we deduce a priori estimates and well posedness for the pure boundary value problems (BVP) on a half-space associated to this class of equations. The initial boundary value problem (IBVP) is investigated too for the special case of the Schrödinger equation, and possible generalizations of the proof for other problems are indicated.